The first 18 issues were co-published by Andrew Brown and Irwin Hirsh. In 1983, Roger Weddall joined the editorial team, and by 1984 he was the sole editor. By 1986 he had gained a new co-editor in Peter Burns and in 1987 the two editors won the Ditmar Award for Best Fanzine.

In the early 1990s, Thyme was edited by LynC and Clive Newall. In 1994, with issue 96, Thyme was accompanied by Australian SF News. beginning with issue 57 of this publication. By 1995 Alan Stewart had taken over the fanzine and won the Ditmar Award for Best Fanzine that year, and again in 1997.